# Is rotation of a mirror image allowed in order to determine chirality? Doesn't rotation alter the mirror image of the molecule?

So, chiral molecules are those which have non-superposable mirror images.

trans-1,2-Dimethylcyclopentane is chiral; 2-butanol is chiral; both don't superpose on their mirror image.

Then my book cited 2-propanol as achiral. How?

The mirror image doesn't seem to superpose with the molecule. How can it be achiral then?

Then the book provided a pic where the author showed how 2-propanol is achiral; he rotated the mirror image & then superposed! Done! 2-propanol is achiral!

But really how can rotation be allowed? After all the mirror image is a stereo-isomer; if it is rotated, wouldn't it be changed?

I'm not getting, why rotation is allowed before superposition. Not every-time, the mirror image is rotated before superposition.

Can anyone please explain how rotation is allowed before superposition?

• superposition is pertinent only to the chiral centers. – A.K. Dec 28 '15 at 5:02
• Molecules in the nature do rotate all the time, come to think of it. – Ivan Neretin Dec 28 '15 at 5:59

As a rule of thumb, in order for a molecule to be chiral, it must have a chiral center. There are some exceptions. A chiral center is a generalized extension of an asymmetric carbon atom, which is a carbon atom bonded to four different entities.

Carbon-2 in 2-propanol is not a chiral center because it is only bonded to 3 unique substituent groups: ($\ce{-H}$), ($\ce{-OH}$), and 2 ($\ce{-CH3}$).

he rotated the mirror image & then superposed! Done!! 2-propanol is achiral!!

You seem to misunderstand. Mirror images of chiral molecules are non-superposable, and mirror images of achiral molecules are superposable (because they are the same molecule).

Rotating the molecule only means orienting a molecule differently in 3-D space, not changing anything about the molecule itself. I'd recommend playing around with a molecule building set to solidify this in your mind.

When checking out chirality or achirality you are always allowed and supposed to rotate the molecule freely in all dimensions. Essentially, what you are trying to prove, is that the mirror image of a molecule can be achieved by rotation alone.

The thought behind this is simple. Chirality is macroscopically proven by optical activity. If you reduce the experiment to its bare basics, you have a polarised light beam that passes through a solution and hits a single molecule to be deflected either to the right (dextrorotatory) or to the left (levorotatory). A second molecule it hits which has the same chirality will move it in the same direction by the same amount. If, however, it hits a molecule which is exactly the mirror image of the first, the effect will be cancelled and the plane of polarisation is moved back into the vertical. In a solution containing only one enantiomer of a chiral substance, the beam will never hit a mirror image and thus always be deflected in a certain direction.

If we continue this thought experiment, we realise that molecular motion in solution is random. Thus, a molecule can — if we give it conciousness — move around freely and let it try to assume exactly the mirror image of the previous one. Therefore, we are allowed and encouraged to rotate (but not to use another mirror image or inversion!) our molecule until it ‘fits’.

By the way, most if not all achiral compounds can also be rotated before you apply the plane of symmetry. Oftentimes if not always, you can rotate them in a way that you see the plane of symmetry present in the molecule itself. If you managed to do that, you won, because just use a plane parallel to that one for mirror imaging and the image will automatically be identical to its template without further rotation.

The plane of symmetry in isopropanol cuts through the $\ce{CHOH}$ bit of isopropanol, dissecting each of those four atoms into two half-spheres. One methyl group will be transformed exactly onto the other by this plane.

• I know that this post is like 2 years old now, but can we rotate about a sigma bond before superimposition? I don't want to ask a separate question as it might be marked a duplicate... – AbhigyanC Nov 3 '17 at 15:52
• @Abhigyan Yes you can. Both before and after. If rotation around sigma bonds will determine that your molecule is achiral, it does not matter whether you rotate until you find a plane of symmetry or if you create the mirror image first and check by rotation if it fits later. – Jan Nov 3 '17 at 16:08

A chiral centre has 4 different atoms or groups attached to it. 2-propanol has two $\ce{CH3}$ groups attached to the second carbon, therefore it does not exhibit stereoisomerism.

Rotating a molecule about an axis so that it can be superimposed on its mirror image does not change its chemistry. If a molecule can be superimposed on its mirror image without having to make/break bonds to reform it, then it does not exhibit stereoisomerism.